My digital camera is eating up batteries while it's off. What is the problem ?

Do I have a short ? How can I fix this problem ?

If you have a short, the batteries would discharge much earlier. Probably the switch to turn of the camera is not switching the camera off. You did not mention what kind of camera so I am not sure what steps you need to take.

However as suggested by all before me, you could take the batteries out when you are not shooting.

I suggest you do the following:
1. Ensure that the battery compartment is clean - no battery leakage lying around and no dust or dirt around the battery terminals.

2. ceck the on-off switch and see if it behaving any different from before. Check if it needs to be changed.

3. If the camera is suppsed to go off when you close a cover, may be the micro-switch that is upposed to switch the camera off is broken. Take it to a camera repair shop (if it is worth the price).

take the batteries out when it is not being used

Yup, that's what I was going to say. Take out your batteries.

Plus I use rechargeable batteries for mine. Batteries started to become ridiculously expensive for my camera.

Turn the batteries upside down when not in use, but just get it checked to make sure it does not have a short!

you keep leaving the batteries in it.

Use rechargable batteries!!

Mine took like four pictures with flash, then the batteries were completely dead. Every time. So I went with Walmart's $9.98 recharger and lithium batteries (get the strongest, 1000 if possible). It saves battery money!